Estimating differential latent variable graphical models with applications to brain connectivity
Abstract
Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, and thus are of particular interest for scientific investigations. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.
Type
Publication
Biometrika, 108(2)
Authors
PhD (2016-2021)
Sen Na was a PhD student in the Department of Statistics at The University of Chicago. Prior to graduate school, he obtained BS in mathematics at Nanjing University, China. His research interests lie in nonlinear and nonconvex optimization, dynamic programming, high-dimensional statistics and their interface.
Authors
Professor of Data Sciences and Operations
Mladen Kolar is a Professor of Data Sciences and Operations at the University of Southern California Marshall School of Business and a Visiting Professor of Statistics and Data Science at Mohamed bin Zayed University of Artificial Intelligence. Before joining USC, he was on the faculty of the University of Chicago Booth School of Business. His research is focused on high-dimensional statistical methods, graphical models, varying-coefficient models and data mining, driven by the need to uncover interesting and scientifically meaningful structures from observational data. He is a Fellow of the Institute of Mathematical Statistics.